Evaluating Expressions and Combining Like Terms

1. Evaluating Expressions and Combining Like Terms R. Portteus

2. Evaluating Expressions • Vocabulary: • Variable – A symbol, usually a letter of the alphabet, such as the letter n, that is used to represent a number. • Variable expression (A.K.A. - Algebraic Expression) – An expression, such as n – 5, that consists of one or more numbers and variables along with one or more arithmetic operations. (Note: No equal sign) • Evaluate a Variable Expression – write the expression, substitute a number for each variable, and simplify the result.

3. How do you describe a variable expression?

4. Evaluate a Variable Expression • Example 1: Evaluate each expression when n = 4. a. n + 3 n + 3 = 4 + 3 = 7 b. n – 3 n – 3 = 4 – 3 = 1 Simplify (means to solve the problem or perform as many of the indicated operations as possible.) Solution: Substitute 4 for n. Simplify Substitute 4 for n. Simplify Solution:

5. Evaluate an Algebraic Expression • Example 2: Evaluate each expression if x = 8. a. 5x 5x = 5(8) = 40 b. x ÷ 4 x ÷ 4 = 8 ÷ 4 = 2 Substitute 8 for x. Simplify Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8. Solution: Substitute 8 for x. Simplify Solution: Recall that division problems are also fractions – this problem could be written as:

6. Evaluating More Expressions • Example 3: Evaluate each expression if x = 4, y = 6, and z = 24. a. 5xy 5xy = 5(4)(6) = 120 b. = 4 Substitute 4 for x; 6 for y. simplify Solution: Substitute 24 for z; 6 for y. Simplify. Solution:

7. Now You Try…Evaluate each expression given that a = 6, b = 12, and c = 3. • 4ac • a ÷ c • a + b + c • ba • b – c • c ÷ b A A A A A A

8. You Try #1 Evaluate each expression given that a = 6, b = 12, and c = 3. • 4ac 4ac = 4(6)(3) = (24)(3) = 72 Substitute the value for a = 6 and c = 3 into the problem and multiply Click to return to “You try it” slide

9. You Try #2 Evaluate each expression given that a = 6, b = 12, and c = 3. 2. a ÷ c a ÷ c = 6 ÷ 3 = 2 Substitute the value for a = 6 and c = 3 into the problem and divide Click to return to “You try it” slide

10. You Try #3 Evaluate each expression given that a = 6, b = 12, and c = 3. • a + b + c a + b + c = 6 + 12 + 3 = 18 + 3 = 21 Substitute the value for a = 6, b=12, and c = 3 into the problem, then add. Click to return to “You try it” slide

11. You Try #4 Evaluate each expression given that a = 6, b = 12, and c = 3. 4. ba ba = (12)(6) = 72 Substitute the value for b=12 and a = 6 into the problem, then multiply. Click to return to “You try it” slide

12. You Try #5 Evaluate each expression given that a = 6, b = 12, and c = 3. 5. b - c b – c = 12 – 3 = 9 Substitute the value for b=12 and a = 3 into the problem, then subtract. Click to return to “You try it” slide

13. You Try #6 Evaluate each expression given that a = 6, b = 12, and c = 3. 6. c ÷ b Substitute the value for c=3 and b = 12 into the problem, then Divide Note: It is better to rewrite this division problem as a fraction. This fraction can now be reduced to its simplest form. Divide both numerator and denominator by the GCF = (3) to reduce this fraction. It is OK to have a fraction as an answer. Click to return to “You try it” slide

14. Combining Like Terms • Now that we have seen some algebraic expressions, we need to know how to simplify them. • Vocabulary • Like terms: In an expression, like terms are the terms that have the same variables, raised to the same powers (same exponents). • i.e. 4x and -3x or 2y2 and –y2 • Coefficient: A constant that multiplies a variable. • i.e. the 3 in 3a or the -1 in –b

15. Combining Like Terms • In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! • To simplify an expression we collect like terms. Like terms include letters that are the same and numbers.

16. Let’s try one… • Step One: Write the expression. 4x + 5x -2 - 2x + 7 • Collect all the terms together which are alike. Remember that each term comes with an operation (+,-) which goes before it. 4x, 5x, and -2x -2 and 7 • Simplify the variable terms. 4x+5x-2x = 9x-2x = 7x • Simplify the constant (number) terms. -2+7 = 5 • You have a simplified expression by writing all of the results from simplifying. 7x + 5

17. Another example… • 10x – 4y + 3x2 + 2x – 2y 3x2 10x, 2x -4y – 2y • 3x2+ 12x– 6y Remember you cannot combine terms with the same variable but different exponents.

18. Now you try… Simplify the following: • 5x + 3y - 6x + 4y + 3z • 3b - 3a - 5c + 4b • 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4 • 5xy – 2yx + 7y + 3x – 4xy + 2x A A A A

19. You Try #1 • Simplify the following: • 5x + 3y - 6x + 4y + 3z 5x, -6x 3y, 4y 3z -x+ 7y+ 3z

20. You Try #2 • Simplify the following: • 3b - 3a - 5c + 4b 3b, 4b -3a -5c -3a+ 7b – 5c

21. You Try #3 • Simplify the following: • 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4 4ab, -ab -2a2b, 2a2b 5, 4 ab2 3ab+ ab2+ 9

22. You Try #4 • Simplify the following: • 5xy – 2yx + 7y + 3x – 4xy + 2x 5xy, -2yx, -4xy 7y 3x, 2x -xy+ 7y+ 5x

23. Conclusion • A variable or algebraic expression is an expression that consists of one or more ________ and _________ along with one or more ________ _________. (Note: No _______ sign) • To evaluate an expression write the _________, substitute a _______ for each variable, and _________ the result. numbers variables arithmetic operations equal expression number simplify

24. Conclusion Continued… • In an expression, __________ are the terms that have the same ________, raised to the same ________ (same exponents). • A coefficient is a number that ________ a variable. like terms variables power multiplies

25. “Your Turn” • 2x – 3x + 6x = 35 • 4r – 8r – 2r = 36 • -5s – 2s – s = -16 • -2y + 6y – 3y = 34 • 13a – 6a – 7a – 2a = 10